Variable-Geometry Turbochargers

Thomas Veltman
October 24, 2010

Fig. 1: A cartoon schematic of a turbocharged engine.
Exhaust flows through the tubine, which drives the
compressor, which feeds the engine more air, allowing more
fuel to be burned.

Turbocharger Parts and Function

A turbocharger consists of two fundamental
components, a turbine and a compressor. The function of the turbine is
to scavenge waste exhaust heat and translate it into rotational motion.
This rotational motion is then used to drive the compressor, which
compresses air for the consumption of the engine. The purpose behind
the turbocharger is to overcome the fundamental drawback of the internal
combustion engine, its volumetric efficiency limit. An engine drawing
air in from the atmosphere can only achieve a volumetric efficiency of
up to 100%, meaning that the pressure inside an individual cylinder is
equal to atmospheric pressure while the intake cycle is occurring.
Since the amount of power that can be extracted from an engine is
proportional to the fuel it burns, and the fuel consumption is limited
by the amount of air present in a cylinder, times the number of
cylinders (the so-called "displacement"), the volumetric efficiency
limit effectively constrains the power of the engine. To make an engine
more powerful, one must increase its displacement.

Unfortunately, the consequence to this is that the
engine burns more fuel under all conditions, adversely affecting its
fuel mileage. The turbocharger provides an alternative means of
extracting more power from a given displacement by increasing the
volumetric efficiency to points significantly above 100%. The pressure
in the cylinders is greater than atmospheric, thanks to the compressor
on the turbocharger. One might wonder how this improves the
fuel-economy situation at all. Because of the way gasoline engines are
controlled, it turns out that a turbocharger can be set up to only
function when one wants additional power, so that most of the time, the
turbocharger doesn't adversely affect fuel economy (perhaps a 5%
reduction overall), but when needed, the engine is capable of turning
out significantly more power. [1]

Fuel Economy and Turbocharging

Obviously burning more fuel will produce more power,
but by producing extra power only when needed, overall fuel economy can
be generally conserved. Turbocharging an engine not purpose-built for
the task (i.e. bolting a turbo onto your car) will result in a slight
loss of fuel economy under low-load conditions (i.e. driving along on
the highway and not accelerating), but increase the power output
significantly when the gas pedal is depressed. A reasonable
approximation for power increase is the manifold pressure ratio (PR).
This is the ratio of engine pressure to atmospheric pressure. When the
turbocharger is running, it is creating a PR greater than 1. To
estimate the power output of such a bolt-on setup, simply multiply the
horsepower of the engine before the turbocharger was installed by the PR
the turbocharger produces. A PR of 2 will generate approximately double
the "factory" horsepower. Note, of course, that doubling your
horsepower doubles your fuel consumption, so under load your fuel
economy will be significantly worse. However, the fact that the
turbocharger produces power-on-demand means that the displacement of the
engine can be lowered without sacrificing power when it is desired.

An ideal solution is to produce small engines which
can tolerate high pressure ratios safely, thereby allowing for the
greatest reduction in fuel demand during normal operation without
sacrificing maximum power production. It is a relatively
straightforward engineering task to redesign the engine such that the
intake pressure can be raised. It turns out that lowering the
compression ratio from 11:1 to 8:1 allows a turbocharger to generate a
PR of about 1.6. One could decrease the displacement of the engine by
34% and still achieve the same power. This reduction in compression
ratio results in a 10% loss in efficiency. As mentioned above, the
turbo itself will increase fuel consumption by approximately 5% owing to
exhaust restriction.

It is now useful to examine a real-world example.
The 2001 Honda Civic (ES) has a 1.67L, 127 horsepower engine (with a
compression ratio of 9.9:1), yet only requires about 15 horsepower to
overcome air resistance at 65 miles per hour. [2] However, the engine
performance community suggests that compression ratios of over 11:1 are
safe on pump gas. [3] If one reduces the engine's displacement by 34%,
the approximate power over the whole range of operation will be about
34% less. At 65 miles per hour, the regular engine produces about 55
horsepower. Therefore the turbocharged engine, without the turbo
running at that speed, produces only 37 horsepower. The wasted
horsepower (and thus fuel) has been reduced by approximately 55% by
lowering the displacement. One must then correct for the turbo
restriction and the compression ratio decrease, which will result in a
net 36% reduction in wasted fuel, or a 28% reduction overall.

The Drawback of Traditional Turbochargers

Fig. 2:Effect of A/R ratio on exhaust flow speed and flow capacity.

The turbines driving turbochargers are characterized
by two chief parameters: A/R ratio and turbine radius. The A/R ratio is
the ratio of the Area of the exhaust gas passage to the Radius from the
center of the turbine wheel to the point defining the center of that
area1. Turbochargers are designed such that the A/R ratio is always a
constant: as the exhaust gasses are directed closer towards the turbine
wheel, the area the gas flows through gets smaller. Funneling the
exhaust down into a smaller area produces a higher velocity stream; a
higher velocity stream imparts more power to the turbine wheel. It is
clear, then, that the turbine can drive the compressor at a higher speed
(and thus produce a greater pressure inside the engine) when the A/R
ratio is low. Unfortunately, as gas velocity increases, so does the
exhaust gas pressure. For the same exhaust flow rate from the engine,
the larger A/R will build up less pressure than the smaller A/R. When
designing a real-world system, both of these factors are important.
Using traditional turbochargers, an engine designer would have to
balance desire for high exhaust flow to drive the compressor against low
back-pressure in the exhaust system, which robs the engine of
efficiency, and in extreme cases, significantly reduces the amount of
power that can be gained from an engine.

Effectively, this means that there is a narrow range
of operation of a turbocharger/engine combination in which the system is
capable of putting out significantly more power, with tails at either
end where power is building up or falling off. This distribution of
power is pivotal to the individuals that actually sell the cars, since
they have to show people on test-drives that the car is a powerful one.
Unfortunately, because of the relationship between A/R ratio and exhaust
flow, a designer must choose between having a quick onset of power
(which subsequently robs the engine of power at higher speeds) or a slow
onset of power (which results in a more powerful car at higher speeds).
Typically, manufacturers interested in selling a lot of cars will choose
the former option and cripple the car at high speeds in favor of 0-30
mile-per-hour acceleration. Conversely, manufacturers interested in
selling high-performance cars choose the latter option, which makes the
car seem like it isn't very quick at low speeds, but once on the
highway, the car shines as the turbocharger is functioning in its
optimal range. However, the speeds in which you might want large
amounts of power tend to be between 25 and 70 miles-per-hour, as this is
a reasonable range where you would want to get up to highway speed, or
alternatively pass a slower-moving car on the highway. Therefore, it is
clear that not every turbocharged car is really operating in the true
ideal range, but rather in a range specifically designed to sell a car
to otherwise ignorant buyers.

Variable-Geometry Turbochargers Provide the Solution

Fig. 3:Diagram of Variable Geometry Mechanism in a Holset turbocharger, side-view. Inset shows the front view of the sliding plate-and-vane mechanism. The dashed line is the second fixed plate. Turbine wheel removed for clarity in both images.

The crux of the problem lies in balancing performance
design with A/R ratio. However, a relatively new technology is
available which obviates this need for balance. The variable-geometry
turbocharger has a mechanism by which the inlet area can be varied to
achieve the optimal A/R for a given flow rate. This is achieved by
varying a set of aerodynamic vanes which direct the exhaust gas flow
onto the turbine wheel. I recently had the opportunity to dismantle a
variable geometry turbocharger manufactured by Holset, and I found that
their vanes are fixed to a sliding plate. The vanes and plate can be
moved as a unit so that the plate can partially obstruct the inlet to
the turbine, thus reducing the A/R ratio. This plate can be moved such
that the inlet is almost completely obstructed, or retracted fully to
provide no resistance to flow. The fixed-position blades slide in and
out of cutouts in a second, fixed plate, which is used to ensure that
exhaust can only travel across the blades.

Using this variability, it is possible to keep the
turbine working under virtually all engine speeds. By dropping the A/R
ratio at low engine RPM (when exhaust flow is low), and then increasing
gradually as RPM increases (and thus exhaust flow increases), inlet
velocity can be kept high without increasing exhaust back-pressure
significantly. This, in turn, means that the turbocharger can function
over the entire operating range of the engine. In fact, since a real
engine does not have a flat power curve with respect to RPM, the turbo
could be controlled in such a way to artificially flatten out the curve
so that the engine has the same power output regardless of its speed.
Doing so makes designing a transmission significantly easier, and allows
one to use gear ratios designed for better acceleration, which further
improves the performance of a vehicle.

Fig. 4:Hypothetical power curves for an engine
with and without a variable turbo. Here the turbo is used
to artificially flatten out the power curve.

As discussed above, turbo size and performance are
inextricably linked. Using conventional turbochargers, an engine will
only produce extra power in a certain range, defined by the A/R of the
turbine. This creates dead spots in performance commonly referred to as
"lag". However, with the variable-geometry turbocharger used in place
of a traditional turbocharger, the engine can match the power of the
normally-aspirated engine instantaneously. The driver will notice no
difference in acceleration between the two vehicles (the variable turbo
has no "lag"), but will certainly notice the difference at the gas
pump.

Drivability may seem like a trivial point, however
the variable-turbo has one other main advantage related to its unique
design. A turbocharger effectively scavenges waste heat from the
engine, so a proper design puts the turbo as close to the engine as
possible to minimize heat losses. Unfortunately, the turbo also works
best when there is no restriction on the outlet, and placing the turbo
right after the engine means that one must put catalytic converters and
mufflers after the turbocharger, which significantly reduces the turbo's
ability to operate efficiently. Instead, with the variable-turbo, one
can install the unit after the catalytic converters (the turbo itself
acts as a surprisingly good muffler). Even though some exhaust heat
will be lost, the catalytic converter will maintain some of the heat
(gasoline engine exhaust tends to be about 1500 °F, while a
catalytic converter operates somewhere around 1200-1300 °), and
the sections of pipe between the converter and the turbocharger can be
insulated to further reduce losses. [4,5] The variable-geometry system can
then more than make up for the heat losses incurred, and in fact, this
situation is preferable, because lower turbo temperatures mean that the
turbo needs fewer expensive materials to guard against melted components
and the whole system will be more reliable. The catalytic converters
will still keep the emissions under control, and the turbo can perform
well under those conditions.

Math, For Those So Inclined

The treatment of the Honda Civic is an approximate
one. The density of air was taken to be 1.18 kg/m3, the drag
coefficient was assumed to be 0.32, which is less than the average for a
passenger car, and the frontal area was approximated as a rectangle of
the dimensions published in the 2001 Honda Civic owner's manual. Drag
power is given by the equation [6,7]

Where ρ is the density of air, v is the vehicle
speed, Cd is the drag coefficient, and A is the frontal area.

The power required to overcome air resistance works
out to be about 10.3 kW (14 hp), which I rounded up to 15 hp. The power
an engine produces scales approximately linearly with increasing RPM, up
to the peak power. [8] Using this assumption, the Honda's power at 65
MPH was estimated based on test data from Car and Driver magazine, where
the peak occurs at 6300 RPM, and 65 MPH is 3100 RPM in fifth gear. [9]
Engine efficiency is given by [10]

and pre-ignition cylinder pressure is given by
[11]

where CR is the engine's compression ratio, γ
is the specific heat ratio (1.4 for air), and P0 is the
pressure inside the cylinder at its largest volume.

Other Points to Consider

Modern engines have the benefit of
electronically-controlled fuel injection and spark ignition, which means
that these parameters can be varied to reduce or eliminate undesirable
and destructive events which can occur inside the engine, namely spark
knock. Spark knock occurs when some of the fuel/air mixture inside the
piston explodes much more violently than the rest of the mixture,
resulting in a large pressure spike inside the cylinder, which is
extremely harmful to an engine; spark knock becomes more likely as the
pressure of the cylinder increases. [12] Reducing spark knock can be
achieved by lowering the compression ratio (CR, the ratio of the total
cylinder volume to the compressed cylinder volume), however lowering the
CR decreases an engine's efficiency. Today's engines can operate at a
CR of about 11:1 while still running on regular unleaded gasoline
(increasing the octane rating of gasoline also decreases knock, but
at the expense of fuel price). [3,12]

Since cylinder pressure is an important factor
affecting spark knock, the pre-ignition cylinder pressure can be
estimated based on an engine's compression ratio, and then used as a
proxy for knock threshold. For these modern engines, the resulting
cylinder pressure is about 29 times atmospheric pressure. It should be
noted that there are purpose-built engines that can sustain pressure
ratios that are higher, but I am interested in estimating for the
average engine. If the compression ratio is dropped from 11:1 to 8:1,
the pressure ratio that the engine will tolerate is about 1.6, meaning
that a turbo could pressurize the system to 1.6 times atmospheric
pressure before knock became a problem.